Quantifying resilience using a unique critical cost on road networks subject to recurring capacity disruptions

This paper presents a methodology to quantify resilience of transportation networks that are subject to recurring capacity disruptions. System-optimal total travel time at full-capacities is usually adopted as a performance-benchmark on networks. Capacity degradation results in different capacity combinations, and thus, there can be different travel times. We thus compare the best network performance with an upper bound of network performanceindicating how much disruptions the network can take in before it displaces from a demand-meeting state to a demand-not-meeting stateand construct an index of network resilience. For this, we establish a critical state which is an upper bound of network cost under recurring capacity degradation. We define discrete capacity levels and search for probability values over those levels that would result in a critical state. We formulate the critical state link disruption problem as a minimax optimisation problem, where expected system travel time is maximised with respect to probability of recurrence and minimised with respect to link flow. We prove that the network cost is unique at the critical state, although the critical degradation need not be. We solve the minimax problem using a coevolutionary algorithm. We exemplify the formulation on test networks and quantify the improvement in network resilience by retrofitting the Sioux Falls network.